In a large bowl, whisk together the mustard, vinegar, olive oil and salt.
Using a paring knife, cut off the top and bottom of the oranges. Set each orange on an end and cut away the peel and pith, working top to bottom. Then cut along the membranes to free the segments. Add the segments to the bowl. Squeeze the juice from the membranes into the bowl and discard the membranes.
Add the cucumber, fennel, radicchio, rice and basil to the bowl. Toss to combine. Cover and refrigerate for 1 hour to let the flavors marry. Let sit at room temperature for 20 minutes before serving.